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Miike012
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Miike012 said:
A rational function is a function that can be expressed as the ratio of two polynomial functions, where the denominator is not equal to zero.
To integrate a rational function, first factor both the numerator and denominator into their simplest forms. Then, use partial fraction decomposition to rewrite the rational function as a sum of simpler fractions. Finally, integrate each fraction separately.
Partial fraction decomposition is a method used to express a complex rational function as a sum of simpler fractions. This is done by breaking down the function into its basic components, such as linear or quadratic factors, and writing each term as a separate fraction.
Not all rational functions can be integrated using algebraic methods. Some require more advanced techniques, such as trigonometric substitutions or integration by parts.
If the rational function contains a square root of a quadratic expression, it is often best to use trigonometric substitutions. Integration by parts is usually used when the rational function contains a product of two functions, or when the denominator cannot be easily factored.
